Christiaan Huygens

"The lasting importance of Horologium Oscillatorium stemmed more from its applied mathematics than from its pure mathematics. The next generation of mathematicians spent a great deal of time trying to find curves that satisfied specific physical properties. What other curve, if any, is a tautochrone? What curve does a hanging chain delineate? What shape does a sail take? What is the curve of fastest descent? These were the test cases for the new mathematical technique Leibniz called 'calculus.'"

"...the power of this line [the cycloid] to measure time."

"I believe that we do not know anything for certain, but everything probably."

"I do not mind at all that [Newton] is not a Cartesian provided he does not offer us suppositions like that of attraction."

"One finds in this subject a kind of demonstration which does not carry with it so high a degree of certainty as that employed in geometry; and which differs distinctly from the method employed by geometers in that they prove their propositions by well-established and incontrovertible principles, while here principles are tested by inferences which are derivable from them. The nature of the subject permits of no other treatment. It is possible, however, in this way to establish a probability which is little short of certainty. This is the case when the consequences of the assumed principles are in perfect accord with the observed phenomena, and especially when these verifications are numerous; but above all when one employs the hypothesis to predict new phenomena and finds his expectations realized."

"I had not thought of this regular decrease of gravity, namely that it is as the inverse square of the distance; this is a new and highly remarkable property of gravity."

"I esteem his [Newton's] understanding and subtlety highly, but I consider that they have been put to ill use in the greater part of this work, where the author studies things of little use or when he builds on the improbable principle of attraction."

"A Man that is of Copernicus’s Opinion, that this Earth of ours is a Planet, carry’d round and enlighten’d by the Sun, like the rest of the Planets, cannot but sometimes think, that it’s not improbable that the rest of the Planets have their Dress and Furniture, and perhaps their Inhabitants too as well as this Earth of ours..."

"It's evident God had no design to make a particular Enumeration in the Holy Scriptures, of all the Works of his Creation."

"These Gentlemen must be told, that they take too much upon themselves when they pretend to appoint how far and no farther Men shall go in their Searches, and to set bounds to other Mens Industry; as if they knew the Marks that God has placed to Knowledge..."

"There are many degrees of Probable, some nearer Truth than others, in the determining of which lies the chief exercise of our Judgment."

"Here we may mount from this dull Earth, and viewing it from on high, consider whether Nature has laid out all her Cost and Finery upon this small Speck of Dirt."

"We shall be less apt to admire what this World calls Great, shall nobly despise those Trifles the generality of Men set their Affections on, when we know that there are a multitude of such Earths inhabited and adorned as Well as our own."

"Now since in so many Things they... agree, what can be more probable than that in others they agree too; and that the other Planets are as beautiful and as well stock'd with Inhabitants as the Earth? Or what shadow of Reason can there be why they should not?"

"Since 'tis certain that Earth and Jupiter have their Water and Clouds, there is no reason why the other Planets should be without them. I can't say that they are exactly of the same nature with our Water; but that they should be liquid their use requires, as their beauty does that they be clear. This Water of ours, in Jupiter or Saturn, would be frozen up instantly by reason of the vast distance of the Sun. Every Planet therefore must have its own Waters of such a temper not liable to Frost."

"What a wonderful and amazing Scheme have we here of the magnificent Vastness of the Universe! So many Suns, so many Earths, and every one of them stock’d with so many Herbs, Trees and Animals, and adorn’d with so many Seas and Mountains! And how must our wonder and admiration be encreased when we consider the prodigious distance and multitude of the Stars?"

"The world is my country, to promote science is my religion."

"Like Hooke, Huygens made fundamental improvements to the clock as a time-keeping mechanism; and Hooke invented the first passable for the same purpose. ...Huygens discovered the rings of Saturn, and the formula for centrifugal force. He did important work in mechanics and optics, and one of his merits was that he made young Leibnitz enthusiastic for these subjects."

"Having converted Galileo's discovery of the isochronism of the pendulum into an accurate timepiece in 1656, Huygens had, in 1662, developed a marine variation employing a short pendulum which had subsequently been subjected to tests at sea with the aid of the English. News of the device having come to Colbert... the new director of France's economic life was determined to secure its advantages for his nation. Accordingly, Huygens was lured to Paris in 1665."

"The academicians—especially in the person of Picard—were carrying through a revolution in observational astronomy made possible by Huygens' astronomical pendulum clock, the filar micrometer perfected (if not invented) by Auzout, and the application of telescopes to large-scale graduated instruments appropriate for the measure of small angles. It was with this equipment that Picard undertook to measure the distance between two localities approximately on the meridian of Paris, to determine the differences in their latitudes, and to deduce from those results the length of degree of meridian. The eminently successful arc measure, marked by a precision thirty to forty times greater than any previously achieved..."

"Mons. Huygens found out a Method whereby the Ball of a Pendulum may be always carried along the Arch of a Cycloid."

"Huygens stated everything verbally when he was in his "geometric mode" and used [mathematical] symbols... only when he switched to his "algebraic mode." Facile mathematician that he was, he switched back and forth between the two modes as his needs changed within the same problem..."

"One of the masterpieces of seventeenth-century scientific literature was... published in 1673 under the title Horologium Oscillatorium (The Pendulum Clock). Much more than a mere description of a clock... it was in fact a treatise on the accelerated motion of a falling body, as exemplified by the bob of a pendulum clock. ...The culminating proposition is Huygen's proof that a body falling along an inverted cycloid reaches the bottom in a fixed amount of time. In other words, the cycloid is isochronous. The third section... introduces his theory of evolutes... that, among other applications, allows one to find the length of a curve. Using evolutes... he proves mathematically that the cycloidal-shaped plates will force the bob of the pendulum to move along the isochronous cycloidal path. The fourth... section... presents his theory of the compound pendulum, in which the motion of a pendulum with mass distributed along its length is compared with that of an ideal simple pendulum... The last part of the book introduces... a variant of a conical clock in which the pendulum, instead of swinging, rotates about a vertical axis... kept on an isochronous path... by the theory of evolutes."

"This [Horologium Oscillatorium] is the first modern treatise in which a physical problem is idealized by a set of parameters then analyzed mathematically. It is one of the seminal works of applied mathematics."

"Foremost, Huygens gave us precise time. His clocks were the first timekeepers to be accurate enough to be reliable in scientific experiments."

"In der wahren Philosophie, führt man die Ursache aller natürlichen Wirkungen auf mechanische Gründe zurück. Dies muss man meiner Ansicht nach thun, oder völlig auf jede Hoffnung verzichten, jemals in der Physik etwas zu begreifen."